A025960 Expansion of 1/((1-2*x)*(1-4*x)*(1-5*x)*(1-8*x)).

1, 19, 235, 2415, 22491, 197799, 1679875, 13959055, 114403531, 929407479, 7508252115, 60439364895, 485415209371, 3892957335559, 31192373841955, 249784713973935, 1999514917852011, 16002339732726039, 128049957250049395, 1024556404696890175, 8197237170079803451

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (19,-126,344,-320).

Formula

a(n) = (8^(n+3)-8*5^(n+3)+9*4^(n+3)-2^(n+4))/72. [Yahia Kahloune, May 25 2013]

a(n) = (4^(n+1)-2^(n+1))/2+13*a(n-1)-40*a(n-2). - Vincenzo Librandi, Jun 01 2026

Mathematica

CoefficientList[Series[1/((1-2*x)*(1-4*x)*(1-5*x)*(1-8*x)), {x, 0, 30}], x] (* Harvey P. Dale, Apr 02 2020 *)
(* Alternative: *)
a[0]=1; a[1]=19; Do[a[n]=(4^(n+1)-2^(n+1))/2+13*a[n-1]-40*a[n-2], {n, 2, 22}]; Table[a[n], {n, 0, 22}] (* Vincenzo Librandi, Jun 01 2026 *)

Prog

(Magma) I:=[1, 19]; [n le 2 select I[n] else (4^n-2^n)/2+13*Self(n-1)-40*Self(n-2): n in [1..22]]; // Vincenzo Librandi, Jun 01 2026

Crossrefs

Sequence in context: A135487 A025965 A276201 * A152494 A171158 A022033

Adjacent sequences: A025957 A025958 A025959 * A025961 A025962 A025963

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved